Answer:
Centre, ((1+10)/2,(6+6)/2)
or, (11/2,12/6)
or, (5.5,6)
Radius,
[√{(10-1)²+(6-6)²}]/2
= (√81)/2
= 9/2 = 4.5
(x-11/2)²+(y-6)²=20.25
Question 19 of 28
Which of the following equations can be used to find the length of BC in the
triangle below?
B
10
А
30
с
A. BC = 30 + 10
B. (BC)2 = 102 + 302
C. BC = 30 - 10
D. (BC)2 = 302 - 102
Answer:
BC^2=10^2+30^2
Step-by-step explanation:
P=10B=30Using pythagorean theorem
[tex]\\ \sf\longmapsto BC^2=10^2+30^2[/tex]
[tex]\\ \sf\longmapsto BC^2=100+300[/tex]
[tex]\\ \sf\longmapsto BC^2=400[/tex]
[tex]\\ \sf\longmapsto BC=\sqrt{400}[/tex]
[tex]\\ \sf\longmapsto BC=20[/tex]
If 5000 is divided by 10 and 10 again what answer will be reached
Hey there!
First, divide 5,000 by 10. You will get 500.
Now, 500 ÷ 10, and you will get your answer, 50.
Hope this helps! Have a great day!
Charity is planting trees along her driveway, and she has 6 pine trees and 6 willows to plant in one row. What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other
Answer:
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the elements are arranged, so we have to use the arrangements formula.
Arrangements formula:
The number of possible arrangements of n elements is:
[tex]A_{n} = n![/tex]
Desired outcomes:
Pine trees(6!) then the willows(6!) or
Willows(6!) then the pine trees(6!). So
[tex]D = 2*6!*6! = 1036800 [/tex]
Total outcomes:
12 trees, so:
[tex]T = 12! = 479001600 [/tex]
What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other?
[tex]p = \frac{D}{T} = \frac{1036800 }{479001600 } = 0.0022[/tex]
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
A company wants to decrease their energy use by 17%. If their electric bill is currently $2500 a month, what will their bill be if they are successful
Find the area of a triangle with the given description. (Round your answer to one decimal place.)
a triangle with sides of length 14 and 28 and included angle 20°
9514 1404 393
Answer:
67.0 square units
Step-by-step explanation:
The formula for the area is ...
Area = 1/2ab·sin(C)
Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units
The area of the triangle is about 67.0 square units.
The length of a rectangle is 10 yd less than three times the width, and the area of the rectangle is 77 yd^2. Find the dimensions of the rectangle.
Answer:
W=7 and L=11
Step-by-step explanation:
We have two unknowns so we must create two equations.
First the problem states that length of a rectangle is 10 yd less than three times the width so: L= 3w-10
Next we are given the area so: L X W = 77
Then solve for the variable algebraically. It is just a system of equations.
3W^2 - 10W - 77 = 0
(3W + 11)(W - 7) = 0
W = -11/3 and/or W=7
Discard the negative solution as the width of the rectangle cannot be less then 0.
So W=7
Plug that into the first equation.
3(7)-10= 11 so L=11
Solve the system of equations.
6x−y=−14
2x−3y=6
whats the answer please C:
Answer:
Step-by-step explanation:
Select the statement that best justifies the conclusion based on the given information.
If a(b + c) = d, then ab + ac = d.
associative
commutative
distributive
closure
Answer:
distributive
Step-by-step explanation:
a(b + c)=ab + ac
it's distributive one
Write the equation of the line that passes through the points (- 5, 1) and (2, 0) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line
Pls help me with this one:(
Answer:
y=-1/7x + 12/7
Step-by-step explanation:
Start by finding the slope
m=(1-0)/(-5-2)
m=-1/7
next plug the slope and the point (-5,1) into point slope formula
y-y1=m(x-x1)
y1=1
x1= -5
m=-1/7
y- 1 = -1/7(x - -5)
y-1=-1/7(x+5)
Distribute -1/7 first
y- 1=-1/7x + 5/7
Add 1 on both sides, but since its a fraction add 7/7
y=-1/7x + (5/7+7/7)
y=-1/7x+12/7
Answer:
Step-by-step explanation:
(-5,1) (2,0)
m=(y-y)/(x-x)
m = (0-1)/2- -5)
m = -1/7
(2,0)
y-0= -1/7 (x-2)
y = -1/7x + 2/7
4) The measure of the linear density at a point of a rod varies directly as the third power of the measure of the distance of the point from one end. The length of the rod is 4 ft and the linear density is 2 slugs/ft at the center, find the total mass of the given rod and the center of the mass
Answer:
a. 16 slug b. 3.2 ft
Step-by-step explanation:
a. Total mass of the rod
Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x
So, λ ∝ x³
λ = kx³
Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,
k = λ/x³ = λ/(L/2)³ = 8λ/L³
substituting the values of the variables into the equation, we have
k = 8λ/L³
k = 8 × 2/4³
k = 16/64
k = 1/4
So, λ = kx³ = x³/4
The mass of a small length element of the rod dx is dm = λdx
So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft
M = ∫₀⁴dm
= ∫₀⁴λdx
= ∫₀⁴(x³/4)dx
= (1/4)∫₀⁴x³dx
= (1/4)[x⁴/4]₀⁴
= (1/16)[4⁴ - 0⁴]
= (256 - 0)/16
= 256/16
= 16 slug
b. The center of mass of the rod
Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm = λxdx = (x³/4)xdx = (x⁴/4)dx.
We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft
The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod
= (1/4)∫₀⁴x⁴dx/M
= (1/4)[x⁵/5]₀⁴/M
= (1/20)[x⁵]₀⁴/M
= (1/20)[4⁵ - 0⁵]/M
= (1/20)[1024 - 0]/M
= (1/20)[1024]/M
Since M = 16, we have
x' = (1/20)[1024]/16
x' = 64/20
x' = 3.2 ft
a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. O c) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.
Answer:
a) Everyone on the team talks until the entire team agrees on one decision.
Step-by-step explanation:
Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense
If (4x-5) :(9x-5) = 3:8 find the value of x.
Answer:
x is 5
Step-by-step explanation:
[tex] \frac{4x - 5}{9x - 5} = \frac{3}{8} \\ \\ 8(4x - 5) = 3(9x - 5) \\ 32x - 40 = 27x - 15 \\ 5x = 25 \\ x = \frac{25}{5} \\ \\ x = 5[/tex]
Step-by-step explanation:
as you can see as i solved above. all you need to do was to rationalize the both equations
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and a third side is 22 more than the length of the shortest side. Find the dimensions if the perimeter is 182 feet.
Answer:40, 80 and 62
Step-by-step explanation:
182-22= 160
160/4 = 40 so,
Shortest side is 40
Longest is 80
Third side is 62
Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.)
(x − 1)y'' − xy' + y = 0, y(0) = −7, y'(0) = 3
You're looking for a solution of the form
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n[/tex]
Differentiating twice yields
[tex]\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n[/tex]
[tex]\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n[/tex]
Substitute these series into the DE:
[tex]\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:
[tex]\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0[/tex]
which indicates that the coefficients in the series solution are governed by the recurrence,
[tex]\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}[/tex]
Use the recurrence to get the first few coefficients:
[tex]\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}[/tex]
You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,
-7 = -7/0!
-7/2 = -7/2!
-7/6 = -7/3!
and so on, with only the coefficient in the n = 1 position being the odd one out. So we have
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots[/tex]
which looks a lot like the power series expansion for -7eˣ.
Fortunately, we can rewrite the linear term as
3x = 10x - 7x = 10x - 7/1! x
and in doing so, we can condense this solution to
[tex]\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}[/tex]
Just to confirm this solution is valid: we have
y = 10x - 7eˣ ==> y (0) = 0 - 7 = -7
y' = 10 - 7eˣ ==> y' (0) = 10 - 7 = 3
y'' = -7eˣ
and substituting into the DE gives
-7eˣ (x - 1) - x (10 - 7eˣ ) + (10x - 7eˣ ) = 0
as required.
use induction method to prove that 1.2^2+2.3^2+3.4^2+...+r(r+1)^2= n(n+1)(3n^2+11n+10)/12
Base case (n = 1):
• left side = 1×2² = 4
• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4
Induction hypothesis: Assume equality holds for n = k, so that
1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12
Induction step (n = k + 1):
1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²
= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²
= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)
= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))
= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)
= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)
On the right side, we want to end up with
(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12
which suggests that k + 2 should be factor of the cubic. Indeed, we have
3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)
and we can rewrite the remaining quadratic as
3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10
so we would arrive at the desired conclusion.
To see how the above rewriting is possible, we want to find coefficients a, b, and c such that
3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c
Expand the right side and collect like powers of k :
3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c
==> a = 3 and 2a + b = 17 and a + b + c = 24
==> a = 3, b = 11, c = 10
HURRY plSSSSSSSSSSSSSSSSSSSSSS
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is eighty degrees and the other is unknown.
Answer:
The unknown is 100
Step-by-step explanation:
A straight line is 180 degrees
We have two angles x, and 80
x+80 = 180
x = 180-80
x= 100
Find m
a 24.7
b 79.2
c 68.3
d 57.4
e 46.5
f 80.1
g 35.6
Answer:
68.3 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan I = opp side / adj side
tan I = sqrt(82) / sqrt(13)
tan I = sqrt(82/13)
Taking the inverse tan of each side
tan ^-1 ( tan I) = tan ^-1( sqrt(82/13))
I = 68.2892
Rounding to the nearest tenth
I = 68.3 degrees
An electrician charges a fee of $40 plus $25 per hour. Let y be the cost in dollars of using the electrician for x hours. Choose the correct equation.
y = 40x - 25
y = 25x + 40
y = 25x - 40
y = 40x + 25
Answer:
y = 25x + 40
Step-by-step explanation:
The electrician charges $25 per hour.
The number of hours is x.
Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)
Therefore fee(y) charged by the electrician = $40 + $25x
Hence y = 25x + 40
A.) Evaluate f(1)
B.) given: f(x) =1, find x
Answer:
f(1) = -2
f(x) =1 when x=0 or x=-2
Step-by-step explanation:
f(1) is the y value when x=1
f(1) = -2
f(x) = 1 means find the x value when y=1
when y =1, x =0 and -2
Determine whether each relation is a function. Give the domain and range for each relation.
{(3, 4), (3, 5), (4, 4), (4, 5)}
Answer:
Not a function
Domain: {3,4}
Range: {4,5}
Step-by-step explanation:
A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function
For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function
Now let's find the domain and range.
Domain is the set of x values in a relation.
The x values of the given relation are 3 and 4 so the domain is {3,4}
The range is the set of y values in a relation
The y value of the given relation include 4 and 5
So the range would be {4,5}
Notes:
The values of x and y should be written from least to greatest when writing them out as domain and range.
They should be written inside of brackets
Do not repeat numbers when writing the domain and range
find the value of the trigonometric ratio
Answer:
15/17
Step-by-step explanation:
sinA = CB/CA =15/17
Answer:
15/17Step-by-step explanation:
sine = opposite / hypotenusesin A = BC/ACsin A = 15/17Customers receive rewards pints based on the purchase type:
11
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
O A. In 2 – In x
OB. 1 + In 2 - In x
Oc. In 2 + In x
OD. In 1 + In 2 - In
Reset
Next
Answer:
B. 1 + ln 2 - ln x
General Formulas and Concepts:
Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex] Logarithmic Property [Dividing]: [tex]\displaystyle log(\frac{a}{b}) = log(a) - log(b)[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle ln(\frac{2e}{x})[/tex]
Step 2: Simplify
Expand [Logarithmic Property - Dividing]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2e) - ln(x)[/tex]Expand [Logarithmic Property - Multiplying]: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + ln(e) - ln(x)[/tex]Simplify: [tex]\displaystyle ln(\frac{2e}{x}) = ln(2) + 1 - ln(x)[/tex]Rewrite: [tex]\displaystyle ln(\frac{2e}{x}) = 1 + ln(2) - ln(x)[/tex]On Halloween, a man presents a child with a bowl containing eight different pieces of candy. He tells her that she may have three pieces. How many choices does she have
Answer:
[tex]56[/tex] choices
Step-by-step explanation:
We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy does not matter.
To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.
Anyways, back to the solving! Remember that the combination formula is
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex], where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.
In this case, [tex]n=8[/tex] and [tex]r=3[/tex]. Substituting these values into the formula gives us:
[tex]_8C_3=\frac{8!}{3!5!}[/tex]
[tex]= \frac{8*7*6*5*4*3*2*1}{3*2*1*5*4*3*2*1}[/tex] (Expand the factorials)
[tex]=\frac{8*7*6}{3*2*1}[/tex] (Cancel out [tex]5*4*3*2*1[/tex])
[tex]=\frac{8*7*6}{6}[/tex] (Evaluate denominator)
[tex]=8*7[/tex] (Cancel out [tex]6[/tex])
[tex]=56[/tex]
Therefore, the child has [tex]\bf56[/tex] different ways to pick the candies. Hope this helps!
An expression is shown below:
6x2y − 3xy − 24xy2 + 12y2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Given:
The given expression is:
[tex]6x^2y-3xy-24xy^2+12y^2[/tex]
To find:
Part A: The expression by factoring out the greatest common factor.
Part B: Factor the entire expression completely.
Solution:
Part A:
We have,
[tex]6x^2y-3xy-24xy^2+12y^2[/tex]
Taking out the highest common factor 3y, we get
[tex]=3y(2x^2-x-8xy+4y)[/tex]
Therefore, the required expression is [tex]3y(2x^2-x-8xy+4y)[/tex].
Part B:
From part A, we have,
[tex]3y(2x^2-x-8xy+4y)[/tex]
By grouping method, we get
[tex]=3y(x(2x-1)-4y(2x-1))[/tex]
[tex]=3y(x-4y)(2x-1)[/tex]
Therefore, the required factored form of the given expression is [tex]3y(x-4y)(2x-1)[/tex].
Please help on my hw
Answer:
b. The solution is a non empty set.
Step-by-step explanation:
There are no common elements.
A capark has 34 rows and each row can acommodate 40 cars. If there are 976 cars parked, how many cars can still be parked?
Answer:
384 cars
Step-by-step explanation:
To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:
34 ⋅ 40 = 1360
As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.
1360 - 976 = 384
Therefore, our answer is 384, specifically, 384 cars.
Answer:
384 cars.
Step-by-step explanation:
40 * 34 - 976
= 1360 - 976
= 384.
Identify the slope and y intercept of the line with equation 2y = 5x + 4
Answer:
Slope is 5/2
y-intercept is 2
Step-by-step explanation:
Turn the equation into slope intercept form [ y = mx + b ].
2y = 5x + 4
~Divide everything by 2
y = 5/2x + 2
Remember that in slope intercept form, m = slope and b = y-intercept.
Best of Luck!
Answer:
slope: 2.5
y-intercept: 2
Step-by-step explanation:
First isolate the y variable which changes the equation to y=2.5x+2
The equation of a line is mx + b where m is the slope and b and the
y-intercept. Leading us to conclude that 2.5 is the slope and 2 is the y-intercept.
Air-USA has a policy of booking as many as 22 people on an airplane that can only seat 20 people. (Past studies have revealed that only 82% of the booked passengers actually show up for the flight.) a) Find the probability that if Air-USA books 22 people, not enough seats will be available. Round your answer to 4 decimal places. P ( X > 20 )
Answer:
The answer is "0.07404893".
Step-by-step explanation:
Applying the binomial distribution:
[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]
Calculating the probability for not enough seats:
[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]
[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]
[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]
what percent of 70 is 35
Answer:
50%
Step-by-step explanation:
35 is halve of 70 therefore it is 50%
hope it helps u...........
